The prior art intervertebral fusing device is made up of a hollow cylindrical body provided therein with an empty space in which bone grafts are contained, and with a perforated wall through which the bone grafts make contact with the vertebrae. A fusion system made by SPINTECH Corp. of the United States is a typical example of such a prior art device as referred to above. The afore-mentioned fusion system is an improved product, which was developed on the basis of the inventive concepts disclosed respectively in U.S. Pat. Nos. 4,501,269 and 5,015,247. The cylindrical body of the prior art device is made of a material having a rigidity, which is about 5-10 times greater than that of the human vertebrae. As a result, the implanted cylindrical body of the prior art device is forced to bear almost entirely the stress exerting on the vertebra under treatment, thereby bringing about a poor contact between the vertebra and the bone grafts contained in the cylindrical body. The healing effect of the prior art device is therefore adversely affected. Moreover, the prior art device described above is further defective in design in that it is deficient in differentials in rigidity.